For a given input value $a$, the function $h$ outputs a value $b$ to satisfy the following equation. $3a-5=-4b+1$ Write a formula for $h(a)$ in terms of $a$. $h(a)=$
Explanation: $h(a)$ expresses $b$ as a function of $a$. To arrive at a correct formula, all we have to do is solve the equation for $b$. $ \begin{aligned}3a-5&=-4b+1\\\\ 4b&=6-3a\\\\ b&=\dfrac{6}{4}-\dfrac{3a}{4}\\\\ b&=\dfrac{3}{2}-\dfrac{3}{4}a\end{aligned}$ Therefore, this formula expresses $b$ as a function of $a$ : $ h(a)=\dfrac{3}{2}-\dfrac{3}{4}a$